DLMF:10.17.E4 (Q3173): Difference between revisions

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Revision as of 15:28, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:29, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2aadec
		Property / Symbols used
			Q11428
		Property / Symbols used: Q11428 / rank
			Normal rank
		Property / Symbols used: Q11428 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11428 / qualifier
			xml-id: C10.S1.XMD3.m1bdec
		Property / Symbols used
			Q11426
		Property / Symbols used: Q11426 / rank
			Normal rank
		Property / Symbols used: Q11426 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11426 / qualifier
			xml-id: C10.S1.XMD6.m1bdec
		Property / Symbols used
			Q11427
		Property / Symbols used: Q11427 / rank
			Normal rank
		Property / Symbols used: Q11427 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11427 / qualifier
			xml-id: C10.S1.XMD7.m1cdec
		Property / Symbols used
			Q11442
		Property / Symbols used: Q11442 / rank
			Normal rank
		Property / Symbols used: Q11442 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\delta}}$ \delta
		Property / Symbols used: Q11442 / qualifier
			xml-id: C10.S1.XMD8.m1adec
		Property / Symbols used
			expansion (locally)
		Property / Symbols used: expansion (locally) / rank
			Normal rank
		Property / Symbols used: expansion (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle a_{k}(\nu)}}$ a_{k}(\nu)
		Property / Symbols used: expansion (locally) / qualifier
			xml-id: C10.S17.XMD1.m1bdec
		Property / Symbols used
			DLMF:10.17.E2
		Property / Symbols used: DLMF:10.17.E2 / rank
			Normal rank
		Property / Symbols used: DLMF:10.17.E2 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\omega}}$ \omega
		Property / Symbols used: DLMF:10.17.E2 / qualifier
			xml-id: C10.S17.XMD2.m1bdec

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Latest revision as of 15:29, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.17.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle Y_{\nu}\left(z\right)\sim\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\*\left(\sin\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{a_{2k}(\nu)}{z^{2k}}+\cos\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{a_{2k+1}(\nu)}{z^{2k+1}}\right),}}$

0 references

DLMF id

DLMF:10.17.E4

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}$

0 references

Symbols used

Bessel function of the second kind

Defining formula

${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E3.m2adec

0 references

Q10931

Defining formula

${\displaystyle{\displaystyle\sim}}$

xml-id

C2.S1.SS3.p1.m11aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2abdec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2aadec

0 references

Q10817

Defining formula

${\displaystyle{\displaystyle\operatorname{ph}}}$

xml-id

C1.S9.E7.m1aadec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2aadec

0 references

Q11428

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C10.S1.XMD3.m1bdec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1bdec

0 references

Q11427

Defining formula

${\displaystyle{\displaystyle\nu}}$

xml-id

C10.S1.XMD7.m1cdec

0 references

Q11442

Defining formula

${\displaystyle{\displaystyle\delta}}$

xml-id

C10.S1.XMD8.m1adec

0 references

expansion (locally)

Defining formula

${\displaystyle{\displaystyle a_{k}(\nu)}}$

xml-id

C10.S17.XMD1.m1bdec

0 references

DLMF:10.17.E2

Defining formula

${\displaystyle{\displaystyle\omega}}$

xml-id

C10.S17.XMD2.m1bdec

0 references

 

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